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You don't give us much to work with.
Error messages?
I seem to remember that MSE wont run in safe mode.
It could be possible your PC is already infected and the virus is stopping the download.
I will assume you are downloading from MICROSOFT.com

Options:

Download & Save on another PC.
Copy to flash drive then install on PC with issues.

While you are downloading software to copy to a flash drive you might as well get the following from CNET.
Both of these run in SAFE MODE.
Malwarebytes Anti-malware
Webroot Antivirus - they have a 30day free trial and it cleared a rootkit virus nothing else would find.

If no error is appearing, it just won't execute, then it's possible you've
picked up some malware that's blocking it. Grab your favorite malware
scanner and start hunting. You may have to do this from safe mode.

Genem, have you thoroughly uninstalled the previous antivirus program?
Some are notoriously difficult to remove completely and can interfere with
attempts to run other antivirus products if they are not successfully
removed. There are specialist antivirus uninstallers available on the net or
you could use Revo Uninstaller if you are comfortable with it.

More about my problem loading MSE. A message in a
box titled Windows Installer appeared with these
words: The feature you are trying to use is on a
network resource that is unavailable.
It wants the installation package ms_ambits.msi.
I ran genuine advantage---genuine. Gene

At 05:16 PM 12/29/2011, you wrote:
>Reply from jshepherd on Dec 29 at 6:33 PM
>You don't give us much to work with.
>Error messages?
>I seem to remember that MSE wont run in safe mode.
>It could be possible your PC is already infected
>and the virus is stopping the download.
>I will assume you are downloading from <http://MICROSOFT.com>MICROSOFT.com
>
>Options:
>
>Download & Save on another PC.
>Copy to flash drive then install on PC with issues.
>
>While you are downloading software to copy to a
>flash drive you might as well get the following from CNET.
>Both of these run in SAFE MODE.
>Malwarebytes Anti-malware
>Webroot Antivirus - they have a 30day free trial
>and it cleared a rootkit virus nothing else would find.
>
>Good Luck.
>

If Lee's link doesn't work, I would suspect either:
1) malware on the system. Is there any chance you are installing this because you are wanting to change malware solutions after an infestation?
2) vestiges of a previous anti-malware suite on the system that is blocking it (i.e. if you had Norton installed, you need to run the Norton Removal Tool, not just 'uninstall' it) Anti-malware, in this context, includes anti-adware, etc. Do you have anything like this that might be installed?
3) a third party firewall blocking it.